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Cryptography, Information Theory, and Error-Correction: A Handbook for the 21st Century

Publisher:

John Wiley

Number of Pages:

468

Price:

99.95

ISBN:

0-471-65317-9

The authors call it a handbook, but that calls to mind a heavy reference volume like the Handbook of Chemistry and Physics, something that you would never actually read. But Cryptography, Information Theory and Error-Correction, although encyclopedic, is lively and engaging, written with palpable enthusiasm.

There are three major parts of the book, called â€œMainly Cryptographyâ€, â€œMainly Information Theoryâ€, and â€œMainly Error-Correctionâ€. While these were once considered largely separate disciplines, new research and continuing developments in technology have served to emphasize their deep interconnections. It should be no surprise - Claude Shannonâ€™s pioneering work crossed back and forth through all three areas.

The book is too rich in topics for the reviewer even to mention them all. Letâ€™s just map out elements of the approach and point out some particularly interesting nuggets. The section of cryptography takes us from classical ciphers like the Caesar and VigenÃ¨re ciphers to modern approaches including RSA, DES and quantum encryption systems. A whole chapter is devoted to elliptic curve cryptography. Another chapter describes cryptographic attacks: methods of breaking modern ciphers and compromising cryptographic systems. Beyond issues about conveying information secretly, the authors also address related questions of authentication, identification and the distribution of cryptographic keys. (The key distribution problem is succinctly described by a Catch 22: â€œTo communicate in secret, one must first communicate in secret.â€)

The section on information theory takes a more or less standard approach, but offers a couple of unusual applications. One of them is how to achieve perfect privacy using a scheme with Latin squares. A chapter on biology focuses on the genetic code and looks at DNA as an information channel with a computable channel capacity.

The chapters on error-correction establish the general ideas of error-correction codes and develop some of the tools from finite fields, linear algebra and number theory. After that, the authors discuss linear codes (including Golay and Hamming codes), linear cyclic codes, and Reed-Solomon codes. Maximum Distance Separable (MDS) codes are described and then applied to the sharing of secrets â€“ partitioning a secret among separate parties while maintaining security and enabling reconstruction of the secret from less than all the pieces.

This bookâ€™s strengths are breadth rather than depth, and the clearly communicated sense of interconnections among the parts. There are about three hundred examples and problems with solutions. Prerequisites are limited: basic calculus, the rudiments of linear algebra, some probability, and a little familiarity with groups and fields. There are a few sections (Shannonâ€™s sampling theorem and elliptic curve cryptography, for example) that require some more sophistication. This is a very readable text, one that encourages a reader to dip in and sample the treats.

Bill Satzer (wjsatzer@mmm.com) is a senior intellectual property scientist at 3M Company, having previously been a lab manager at 3M for composites and electromagnetic materials. His training is in dynamical systems and particularly celestial mechanics; his current interests are broadly in applied mathematics and the teaching of mathematics.